In most cases, various steel wire rods are subjected to softening heat treatments such as softening or spheroidizing annealing to decrease the hardness thereof. In such heat treatments as carried out heretofore, the wire rods produced in the rolling step are placed in the coil form in a heat treatment furnace disposed as a separate line where they are heated from normal temperature to 600.degree.-800.degree. C., followed by gradual cooling or heat holding. However, the rate of temperature rise of the wire rod is extremely low in the coiled form, and they should be held for an extended period of time so as to decrease a temperature difference or variation in the outer and inner portions of the coil, and gradually cooled. Occasionally, a prolonged time period of as long as 20 hours or longer may be required for such treatments.
For that reason, it has been proposed in e.g., Japanese Patent Kokai-Publication No. 58-107426 to rapidly heat wire rods in a stranded state and, thereafter, coil up them in a heat-holding furnace with a view of curtailing the treating time. However, such a proposal has the disadvantage that, due to the use of high-frequency heating as the rapid heating means, the consumption of electric powder is so increased that it is costly, although the treating time is curtailed. This proposal poses also another problem that the coiled wire rod easily suffers surface flaws during the transportation from the rolling line to the coiling line after the rolling step.
To this end, direct softening heat treatment processes for softening wire rods by gradually cooling or heat holding them just after rolling, making use of the sensible heat thereof after hot- or warm-rolling, have been proposed in Japanese Patent KoKai-Publication Nos. 56-133445, 58-27926, 58-58235, 58-107416, 59-13024, etc. All these processes involve softening wire rods by a combination of the rolling conditions with the gradual cooling conditions after rolling. Among others, Japanese Patent Kokai-Publication No. 56-133445 teaches that, as illustrated in FIG. 5, once a wire rod M has been wound around a coiler device 1 disposed outside of a gradual cooling furnace 2 after rolling, the obtained coil M' is placed in the cooling furnace. In this process, however, there are considerable variations in the quality of coils after the softening heat treatment, which are attributable on the one hand to temperature variations in the axial direction of the coils based on a difference in the air cooling time from the initiation to the completion of coiling and on the other hand to temperature differences in the radial direction of the coils based on the heat radiation from the surface of the coils. This is because the coils should previously be coiled up outside of the gradual cooling furnace. Furthermore, in a warm-rolling process, e.g., that is finished just at a temperature above the point of Ar.sub.1 transformation, there is a disadvantage that the later gradual cooling only produces a significantly decreased softening effect since Ar.sub.1 transformation is completed during coiling-up.